Number Theory 2025

Covers divisibility, congruences, primes, Diophantine equations & cryptography—designed for college & university student

What you'll learn

Understand and apply the concepts of divisibility, prime numbers, and the Euclidean algorithm.

Solve linear and quadratic congruences using modular arithmetic and Chinese Remainder Theorem.

Analyze and solve Diophantine equations, including linear and binary quadratic forms.

Apply Fermat’s Little Theorem and Euler’s Theorem in mathematical proofs and cryptographic contexts.

Requirements

Academic Level Math knowledge is Required

Set theory

Basic Mathematics

Description

Are you pursuing BSc Mathematics (Hons), BSc Computer Science, BCA, MCA, or preparing for competitive exams like GATE, NET, JAM?Do you want to learn Number Theory from Basic To advance?Do you struggle with tough mathematical topics like congruences, Diophantine equations, or Euler’s theorem?Then you are at the right place!This course is a complete and in-depth guide to Number Theory, a core subject in mathematics with applications in cryptography, computer science, and algorithm design. It has been crafted especially for students at the college/university level, with a clear focus on conceptual understanding and exam preparation.You will learn step-by-step through:Divisibility, primes, GCD, LCMModular arithmetic and congruencesDiophantine equations and number theoretic functionsEuler’s & Fermat’s theoremsApplications in encryption and coding theoryEvery lecture includes examples, explanations, and problem-solving techniques to make learning easy—even if you’re weak in math.Thousands of students find Number Theory difficult. This course simplifies it with real clarity, smart strategies, and well-structured lessons.By the end of this course, you’ll be ready to:Solve university-level problemsAttempt competitive exam questions with confidenceUnderstand modern cryptographic applications based on number theory Start your journey now—master Number Theory and upgrade your academic power!

Overview

Section 1: Divisibility Theory in the Integers

Lecture 1 Definitions

Section 2: Diophantine Equation

Lecture 2 The Diophantine Equation

Lecture 3 Diophantine Equation Solution

Section 3: Primes and Their Distribution

Lecture 4 Prime and its properties

Lecture 5 Prime form

Section 4: Theory of Congruences

Lecture 6 Congruency Theorems

Lecture 7 Basic Properties of Congruences

Lecture 8 Questions Practice on Congruence Properties

Lecture 9 More Questions

Section 5: Fermat Little Theorem

Lecture 10 Concept of Fermat Little Theorem

Lecture 11 Question Practice on Fermat little Theorem part 1

Lecture 12 Practice Question Part 2

Lecture 13 Practice Question Part 3

Section 6: Number Theoretic Functions

Lecture 14 Some important Functions

Lecture 15 Practice Question on Number Theoretic Function

Lecture 16 Theorem on Number Theoretic Function

College Students who have Number theory as a subject in their course,BSC MATHEMATICS,BCA,MCA,BSC COMPUTER SCIENCE STUDENTS,Those who want to learn Number Theory